The present exemplary embodiments are directed to fault diagnosis and more particularly to multiple fault diagnosis. Troubleshooting a practical system to isolate broken components can be difficult, as the number of fault combinations grows exponentially with the number of components. Qualitative reasoning proposed the idea of starting from simple fault assumptions for computationally efficient diagnosis, and escalating to more complicated faulty assumptions when necessary. It may be desirable to extend this idea from qualitative reasoning to quantitative reasoning. However, an issue is whether it is possible to apply statistical inference, which is precise but computationally intense, in a computationally efficient manner.